Among Sen. Cory Booker’s donors to his presidential campaign is a vice president of a leading pharmaceutical company. The senior vice president of Comcast who oversees the company’s lobbying efforts hosted a fundraiser for former vice president Joe Biden. An oil company development and finance manager remains one of former congressman Beto O’Rourke’s most generous donors, including to his presidential campaign.

These Democratic presidential hopefuls accepted these contributions, even though they had rejected the help of fossil fuel, pharmaceutical and lobbying industries.

According to their campaigns, they did nothing wrong, because their pledges cover only a small group of high-level executives and registered lobbyists. But critics see something darker: a willingness by campaigns to bend their own rules, allowing money and influence to seep in.

“If you’re getting large checks from or a substantial number of donations from a particular industry or from a particular company, any opponent is going to start asking questions about how they’re influencing you, and it won’t matter where in the company it’s coming from,” said Basil Smikle, a Democratic strategist and former executive director of the New York State Democratic Party.

Booker (D-N.J.), Biden and O’Rourke are not alone. Every Democratic primary candidate this year has sworn off financial support from certain industries despised by the Democratic base, a reaction to increasing skepticism among voters of the influence of special interests on politics.

Yet federal filings show campaigns have accepted plenty of money from influential donors in those industries — as long as the donor’s job title falls outside the narrow, and at times technical, definitions in candidates’ pledges.

Such donations underscore how campaigns are navigating the expectations of voters and activists while working to draw tens of millions to survive a crowded and lengthy primary. But critics say these contributions show that candidates have taken symbolic pledges with arbitrary definitions.

Candidate financial pledges date at least to 2008, when Barack Obama disavowed donations from federal lobbyists on the heels of the Jack Abramoff scandal.

Today’s promises are much broader, often focusing on specific industries, said Ami Copeland, former deputy national finance director of Obama’s 2008 campaign.

“Who was the boogeyman of the day [in 2008]? It was federal lobbyists,” Copeland said. “I think that title of boogeyman has expanded, and continues to, based on perceived and actual wrongdoings.”

All the highest-polling 2020 candidates have rebuked help from three sources: “fossil fuel money,” federal or corporate lobbyists, and corporate PACs. Some candidates have committed to return money from pharmaceutical executives.

But the pledges come with caveats.

In the case of fossil fuels, candidates have vowed not to accept contributions exceeding $200 from executives, lobbyists and PACs in the oil, gas and coal industry. But they have accepted donations from others in high-level positions at such companies, sometimes in contributions that came in smaller amounts at a time that ultimately added up to several hundred dollars or more than $1,000.

Sen. Kamala D. Harris (D-Calif.) has accepted donations from a top attorney at CITGO Petroleum, among others at natural gas corporations, federal filings show. After an inquiry from The Washington Post, Harris’s campaign said it was in the process of returning a gift from a vice president at Consumers Energy, a Michigan-based natural gas and electricity company.

South Bend, Ind., Mayor Pete Buttigieg has received money from a CITGO manager who is now assistant corporate controller of another Texas-based petroleum distributor.

O’Rourke, a Texas Democrat, has accepted tens of thousands of dollars from the oil and gas industry to his presidential campaign, according to data from the Center for Responsive Politics. O’Rourke’s campaign noted that this data encompasses all donations from the industry, including “everyday employees who are not in the industry’s leadership and are not at odds with the No Fossil Fuel Money pledge.”

Biden received the maximum $2,800 donation from the president of Marathon Energy Corp., a New York-based oil, gas and electricity supplier.

In most of these cases, the candidates did not technically violate their agreements. There are gray areas to these pledges that allow smaller donations from lower-ranking employees in the industries, said Neil Sroka, spokesman for Democracy for America, a liberal political action committee that advocates for less money in politics. Whether candidates allow for wiggle room in their promises reflects their commitment to “stamping out the role that these powerful interests have in our politics,” he said.

“It in some ways helps highlight just how insidious the corporate control of our politics are, and just how much work has to be done to really stamp out the incredibly powerful role that these kind of corporate interests have on our politics,” Sroka said.

Many candidates also have sworn off money from registered federal lobbyists, continuing the trend from the 2008 campaign. Yet that is just one slice of the sprawling influence industry, which is also active at the state level.

In the wake of regulations that increased disclosure requirements and made it more difficult for lobbyists to work in Obama’s administration, the number of registered lobbyists plummeted. But many continued to lobby without registering.

Per federal disclosure regulations, those who spend more than 20 percent of their time lobbying for a single client over three months must register with the federal government. That means campaigns can take donations from state lobbyists and those who work at the intersection of government and corporate interests but are not required to register as a lobbyist.

Many of the top-polling 2020 presidential hopefuls who have taken the pledge — including Harris, Biden, Buttigieg and O’Rourke — have accepted donations from individuals in the influence industry who are not registered federal lobbyists.

Buttigieg has received contributions from donors including former White House official Josh Black, associate vice president for international advocacy at PhRMA, the pharmaceutical industry’s lobbying arm. Biden has taken donations from several government relations specialists, including Denise McGraw, who is not a registered lobbyist but is a partner at the lobbying firm Hill, Gosdeck & McGraw, whose clients include Facebook, AT&T and MillerCoors.

Sen. Elizabeth Warren (D-Mass.), a vocal advocate for greater regulation of moneyed influence in Washington, received $2,800 from the vice president for public policy at Yelp, filings show.

“A weakness with our lobbying rules is that they actually don’t cover many who are integral to the process of what we would think of as lobbying,” said Daniel Weiner, senior counsel for the Democracy Program at the Brennan Center for Justice.

Many of the campaigns — among them, those of Biden, Harris and O’Rourke — said they are careful to return all donations that violate their pledges.

Warren campaign spokeswoman Saloni Sharma reiterated the senator’s objections to the current system for defining lobbyists and added that it is “aggressively enforcing” its campaign finance policies.

Chris Meagher, a Buttigieg campaign spokesman, said, “Our position is clear: We do not take money from registered federal lobbyists, corporate PACs, or fossil fuel company executives.”

A spokesman for Biden said the candidate “is committed to fighting the influence of big money in politics and elevating the voices of the American people over special interests.”

As rising costs of health care and insurance become a focus of the 2020 race, many candidates also have disavowed donations from pharmaceutical industry executives. Earlier this month, Sen. Bernie Sanders (I-Vt.) rolled out a pledge urging candidates to reject contributions of more than $200 from PACs, lobbyists or executives from a long list of health insurance and pharmaceutical companies. But he soon came under fire for accepting funds from some of those very donors; his campaign said it would return all past contributions that did not comply with the pledge.

After receiving criticism for collecting hundreds of thousands of dollars from major pharmaceutical companies, Booker announced in 2017 that he would take a “pause” on donations from the industry.

His policy, according to a spokeswoman, is to reject money from C-suite executives, board chairs, or corporate and industry PACs in the pharmaceutical industry. Booker’s campaign has accepted donations from others in management positions in the industry, such as a maxed-out check from Sonya Kakkar, regional quality head at Pfizer. Booker’s team did not provide a statement.

Ultimately, the Democratic presidential nominee is likely to benefit from donations from all of the industries, despite their pledges during the primary campaign. The Democratic National Committee — which will channel its funds to support the party’s nominee — has not made similar promises.

But for now, candidates are brandishing their campaign finance pledges to create the impression that their campaigns are fueled by grass-roots donations by everyday Americans.

“We’re relying on the support of grass roots donors across the country to power this campaign — not corporate PACs or lobbyists,” the Biden campaign tweeted on the last day of the recent campaign-filing deadline. “Will you chip in before tonight’s end-of-quarter deadline?”